



2, 4, 7, 10, 12, 14, 17, 19, 22, 24, 27, 30, 32, 35, 37, 40, 42, 44, 47, 50, 52, 54, 57, 59, 62, 64, 67, 69, 71, 74, 77, 79, 82, 84, 87, 90, 92, 94, 97, 99, 102, 104, 107, 110, 112, 115, 117, 120, 122, 124, 127, 130, 132, 135, 137, 140, 143, 145, 147, 150
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Conjecture: a(n)/n > 5/2.
Proof of this conjecture: it is equivalent to prove that the frequency of 1 in A285966 exists and equals 2/5.
This follows from my characterization of A285966 as a morphic sequence.
The incidence matrix of that morphism has PerronFrobenius eigenvalue 2, with right eigenvector (1,1,2,1). It follows that the letters 2 and 4 in the fixed point of the morphism have both frequency 1/5. As these are exactly the letters that are mapped to 1 in A285966, the letter 1 has frequency 2/5 in A285966.
(End)


LINKS



EXAMPLE

As a word, A285966 = 01010010010101001010010..., in which 1 is in positions 2,4,7,10,12,...


MATHEMATICA

s = Nest[Flatten[# /. {0 > {0, 1}, 1 > {1, 0}}] &, {0}, 9] (* ThueMorse, A010060 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"11" > "1"}]
st = ToCharacterCode[w1]  48 (* A285966 *)
Flatten[Position[st, 0]] (* A285967 *)
Flatten[Position[st, 1]] (* A285968 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



